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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.09561 |
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Table of Contents:
- In this paper we consider a conilpotent coalgebra $C$ over a field $k$. Let $Υ\colon C\textsf{-Comod}\longrightarrow C^*\textsf{-Mod}$ be the natural functor of inclusion of the category of $C$-comodules into the category of $C^*$-modules, and let $Θ\colon C\textsf{-Contra}\longrightarrow C^*\textsf{-Mod}$ be the natural forgetful functor. We prove that the functor $Υ$ induces a fully faithful triangulated functor on bounded (below) derived categories if and only if the functor $Θ$ induces a fully faithful triangulated functor on bounded (above) derived categories, and if and only if the $k$-vector space $\operatorname{Ext}_C^n(k,k)$ is finite-dimensional for all $n\ge0$. We call such coalgebras "weakly finitely Koszul".